Mechanics Contents
2
Mechanics CONTENTS PREFACE Chapter 1 MODELLING and MECHANICS 1.0 Introduction 1 1.1 Modelling from data 2 1.2 Motion and force 3 1.3 Newton's law of gravitation 8 1.4 Units and dimensions 10 Chapter 2 ONE-DIMENSIONAL MOTION 2.0 Introduction 15 2.1 How to represent motion 16 2.2 Modelling motion under constant acceleration 23 2.3 How do bodies move under gravity? 27 2.4 What causes changes in motion? 30 2.5 How to deal with more than one force 35 2.6 Forming differential equations 40 2.7 Direct integration 42 2.8 What happens during collisions? 44 2.9 Miscellaneous Exercises 48 Chapter 3 VECTORS 1 3.0 Introduction 53 3.1 Vector notation and properties 56 3.2 Relative position vectors 61 3.3 Unit vectors 63 3.4 Vectors in three dimensions 65 3.5 Scalar products 67 3.6 Velocity as a vector 70 3.7 Acceleration as a vector 72 3.8 Instantaneous velocity and acceleration 73 3.9 Investigating the velocity and speed of the ball 77 3.10 Average acceleration of the ball 81 3.11 Miscellaneous Exercises 84 Chapter 4 VECTORS 2 4.1 From acceleration to velocity to position vector 87 4.2 Force as a vector 91 4.3 Resolving forces 93 4.4 Friction 95 4.5 Forces in equilibrium 98 4.6 Non-equilibrium situations 102 4.7 Miscellaneous Exercises 106 Chapter 5 PROJECTILES 5.0 Introduction 109 5.1 Making a mathematical model 110 5.2 Setting up a model for projectile motion 110 5.3 Solving the basic equation of the model 113 5.4 Validating the model 116 5.5 More deductions from the model 123 5.6 Using the model 128 5.7 Miscellaneous Exercises 129 Chapter 6 WORK and ENERGY 6.0 Introduction 133 6.1 Work and kinetic energy 133 6.2 Work done against gravity: gravitational potential energy 140 6.3 Work-energy equation. Conservation of energy 141 6.4 Power 146 6.5 Elasticity - Hooke's Law 150 6.6 Work done in stretching an elastic string 154 6.7 Energy revisited 157 6.8 Using scalar products 164 6.9 Miscellaneous Exercises 167
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Transcript of Mechanics Contents
Mechanics
CONTENTSPREFACE
Chapter 1 MODELLING and MECHANICS
1.0 Introduction 1
1.1 Modelling from data 2
1.2 Motion and force 3
1.3 Newton's law of gravitation 8
1.4 Units and dimensions 10
Chapter 2 ONE-DIMENSIONAL MOTION
2.0 Introduction 15
2.1 How to represent motion 16
2.2 Modelling motion under constantacceleration 23
2.3 How do bodies move under gravity? 27
2.4 What causes changes in motion? 30
2.5 How to deal with more than one force35
2.6 Forming differential equations 40
2.7 Direct integration 42
2.8 What happens during collisions? 44
2.9 Miscellaneous Exercises 48
Chapter 3 VECTORS 1
3.0 Introduction 53
3.1 Vector notation and properties 56
3.2 Relative position vectors 61
3.3 Unit vectors 63
3.4 Vectors in three dimensions 65
3.5 Scalar products 67
3.6 Velocity as a vector 70
3.7 Acceleration as a vector 72
3.8 Instantaneous velocity and acceleration 73
3.9 Investigating the velocity and speedof the ball 77
3.10 Average acceleration of the ball 81
3.11 Miscellaneous Exercises 84
Chapter 4 VECTORS 2
4.1 From acceleration to velocityto position vector 87
4.2 Force as a vector 91
4.3 Resolving forces 93
4.4 Friction 95
4.5 Forces in equilibrium 98
4.6 Non-equilibrium situations 102
4.7 Miscellaneous Exercises 106
Chapter 5 PROJECTILES
5.0 Introduction 109
5.1 Making a mathematical model 110
5.2 Setting up a model for projectilemotion 110
5.3 Solving the basic equation of themodel 113
5.4 Validating the model 116
5.5 More deductions from the model 123
5.6 Using the model 128
5.7 Miscellaneous Exercises 129
Chapter 6 WORK and ENERGY
6.0 Introduction 133
6.1 Work and kinetic energy 133
6.2 Work done against gravity:gravitational potential energy 140
6.3 Work-energy equation.Conservation of energy 141
6.4 Power 146
6.5 Elasticity - Hooke's Law 150
6.6 Work done in stretching an elasticstring 154
6.7 Energy revisited 157
6.8 Using scalar products 164
6.9 Miscellaneous Exercises 167
Mechanics
Chapter 7 CIRCULAR MOTION
7.0 Introduction 171
7.1 Angular velocity and angular speed 172
7.2 Describing motion in a circlewith vectors 175
7.3 Motion in a circle with constantangular speed 180
7.4 Motion on a banked curve 186
7.5 Miscellaneous Exercises 189
Chapter 8 SIMPLE HARMONIC MOTION
8.0 Introduction 191
8.1 Pendulum experiments 191
8.2 Pendulum theory 192
8.3 Energy consideration 195
8.4 Modelling oscillations 197
8.5 Springs and oscillations 200
8.6 Miscellaneous Exercises 204
Chapter 9 PHYSICAL STRUCTURES
9.0 Introduction 207
9.1 Introducing frameworks 208
9.2 Analysis of a simple framework 215
9.3 More complex frameworks 217
9.4 Methods of joints 219
9.5 Lifting devices 222
9.6 Moment of a force 222
9.7 Couples 228
9.8 Contact forces 230
9.9 Stability 232
9.10 The centre of gravity of a body 234
9.11 The centres of gravity of somesimple bodies 236
9.12 The centre of gravity of compositebodies 238
9.13 Some applications of centres ofgravity 242
9.14 Sliding and toppling of a block 244
9.15 Miscellaneous Exercises 249
ANSWERS 253
INDEX 263
